The maximum a posteriori (MAP) decoding algorithm introduced by Bahl, Cocke, Jelinick, and Raviv in "Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate", IEEE Transactions on Information Theory, March 1974, pp. 284-287, also known as the BCJR algorithm, is an optimum symbol-by-symbol decoder for trellis codes. It is particularly useful as a component decoder in decoding parallel concatenated convolutional codes, i.e. turbo codes, because of its excellent performance. It is advantageous for decoding turbo codes because it accepts soft-decision information as an input and produces soft-decision output information. However, one problem with this type of decoder is that it requires a relatively large amount of memory. For example, the entire received code word must be stored during decoding due to the nature of the algorithm. Furthermore, in order to obtain high-speed decoding, it is necessary to store a large number of intermediate results which represent various event probabilities of interest so that they can be combined with other results later in the decoding process, which decoding process comprises forward and backward (from the end to the beginning of a received code word) recursive calculations. The MAP algorithm as described by Bahl et al. requires that at least half of the results from the two recursive calculations be stored in memory for fast decoding.
Memory size is a particular problem in turbo coding systems since bit-error rate is inversely proportional to the number of information bits in the code word. (The term "block size" as used herein refers to the number of information bits in a code word.) In a turbo coding system, therefore, it would be desirable to utilize the largest block size possible in order to obtain the greatest coding gain. Unfortunately, an efficient and practical system utilizing such a large block size has not emerged heretofore.
Therefore, it is desirable to provide a method and system for encoding and decoding large trellis codes, which method and system require a significantly reduced memory without compromising coding gain and without additional overhead. It is furthermore desirable that such a method and system be applicable to turbo coding such that an efficient and practical turbo coding system is realizable.